Earlier, Democrat Jon Tester was declared the winner over Republican Rep. Denny Rehberg in Montana, a contest which saw an estimated $40 million spent in a state with fewer than 1 million residents. See results

Those victories, which gave Democrats control of 53 seats in the Senate -- along with one independent, Bernie Sanders of Vermont, who caucuses with them -- kept the party's edge in the upper chamber of Congress.

Independent Angus King of Maine won an open Senate seat that had been held by Republican Olympia Snowe, NBC News projected. King could vote with the Democrats, though he hasn't yet said which party, if any, he will side with.

In one of the most hotly contested Congressional races, Democrat Elizabeth Warren won the Massachusetts Senate seat held by Republican Sen. Scott Brown, becoming the first woman to be elected to the Senate from that state. The senator-elect speaks with TODAY's Matt Lauer about her victory.

"Things like this are what happens when your No. 1 goal is to defeat the president and not work to get legislation passed," Senate Democratic leader Harry Reid of Nevada said in a statement.

In a statement of his own, Republican leader Mitch McConnell of Kentucky challenged Obama to "propose solutions that actually have a chance of passing the Republican-controlled House of Representatives and a closely divided Senate."

"To the extent he wants to move to the political center, which is where the work gets done in a divided government, we'll be there to meet him halfway," McConnell said.

Democratic former Virginia Gov. Tim Kaine beat former Republican Gov. George Allen, NBC News projected, keeping the seat held by the retiring Sen. Jim Webb in Democratic hands. See results

Democratic Rep. Joe Donnelly of Indiana defeated Republican state Treasurer Richard Mourdock to claim the open seat held by Republican Dick Lugar, NBC News projected. Mourdock had been favored until he drew national opposition for having said in a debate last month that he believed that pregnancies resulting from rape were a "gift from God" and shouldn't be terminated. See results

Democratic Sen. Claire McCaskill held on to her seat in Missouri after Republican Rep. Todd Akin made similar comments in a TV interview in August, suggesting that women's bodies could "shut down" a pregnancy that was the result of a "legitimate rape." See results

Virginia Senator-elect Tim Kaine weighs in on what made the difference for him and the president in his state, how Obama plans to work with the GOP and why it may be a more cooperative relationship in this second term.

Thompson, who served as secretary of Health and Human Services in the administration of former President Geoorge W. Bush, announced his retirement from politics in his concession speech. Wisconsin results

Democrats entered Tuesday with control 53 seats in the current Senate (that number included Sanders and Joe Lieberman of Connecticut, an independent who also generally voted with them); Republicans held 47.

Ten senators weren't seeking re-election this cycle — the most since 1996. In addition, Lugar lost to Mourdock in the Indiana Republican primary, meaning at least 11 new faces will join the Senate on Jan. 2.

Warren's victory was particularly sweet for Democrats, for whom she was a hero as the architect of Obama's U.S. Consumer Financial Protection Bureau.

"You took on the powerful Wall Street banks and special interests, and you let them know you want a senator who will be out there fighting for the middle class all of the time," she told cheering supporters in Boston.

The races in Missouri and Indiana were also closely watched because of the controversies generated by Akin's and Mourdock's comments on abortion.

McCaskill reveled in her victory, giving supporters a beaming I-told-you-so speech in St. Louis.

"They all said it's over — it's done, it's too red, it's just too red," she said. "There is no way that Claire McCaskill can survive. Well, you know what happened? You proved them wrong."

Akin told supporters in Missouri that he had called to congratulate McCaskill, but he sounded a defiant note:

Todd Akin says that called Claire McCaskill to concede after being defeated in the Missouri Senate race.

"I also think, in the circumstances that we've all been through, that it is particularly appropriate to thank God, who makes no mistakes and is wiser than we are," Akin said.